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We develop a novel stochastic primal dual splitting method with Bregmandistances for solving a structured composite problems involving infimalconvolutions in non-Euclidean spaces. The sublinear convergence in expectationof the primal-dual gap is proved under mild conditions on stepsize for thegeneral case. The linear convergence rate is obtained under additionalcondition like the strong convexity relative to Bregman functions.

A Stochastic Variance Reduction Algorithm with Bregman Distances for Structured Composite Problems